Integral-equation methods for all-dielectric gratings

Semi-analytical and numerical methods based on integral equations constitute powerful mathematical tools for the modelling and computational analysis of periodic structures. Specifically, concerning all-dielectric isotropic gratings, integral-equation methods can provide accurate solutions in an efficient manner and within a limited computational time. To this end, they can prove particularly useful in optimizations of the grating's parameters to achieve desired operational functionalities like, e.g. wavelength filtering, anomalous reflection and refraction, and steering of the diffracted waves to desired directions. This article provides an overview of integral-equation methods, including boundary- and volume-integral-equation methods, analytical regularization methods, the extended boundary condition method and methods employing auxiliary sources.This article is part of the theme issue 'Analytically grounded full-wave methods for advances in computational electromagnetics'.